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By Petersen's theorem, a bridgeless cubic graph has a 2-factor. H. Fleis-chner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3-edge-connectivity, we can find a spanning even subgraph in which every component… (More)

Given an integer λ ≥ 2, a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G, H) is a proper vertex coloring V → {1, 2,. . .} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study the case where the backbone is either a collection of pair-wise disjoint stars or a matching.… (More)

By Petersen's theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even sub-graph. Our main result is that every bridgeless simple graph with minimum degree at least 3 has a spanning even subgraph in which… (More)

Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most… (More)

Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V (G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore's theorem which guarantees the existence of a Hamilton path connecting any… (More)

Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex coloring V → {1, 2,. . .} of G in which the colors assigned to adjacent vertices in H differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or… (More)

In this article, we prove that a line graph with minimum degree δ ≥ 7 has a spanning subgraph in which every component is a clique of order at least three. This implies that if G is a line graph with δ ≥ 7, then for any independent set S there is a 2-factor of G such that each cycle contains at most one vertex of S. This supports the conjecture that δ ≥ 5… (More)